What is the derivative of (6x/(x^2-9)) ?

The derivative of (6x/(x^2-9)) is (6(-x^2-9))/((x^2-9)^2)

What is the first derivative of (6x/(x^2-9)) ?

The first derivative of (6x/(x^2-9)) is (6(-x^2-9))/((x^2-9)^2)

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\frac{d}{d x} (\frac{6 x}{x ^{2} - 9})

\frac{6 ( - x ^{2} - 9 )}{( x ^{2} - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x}{x ^{2} - 9})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (\frac{x}{x ^{2} - 9})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 6 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 9 ) - \frac{d}{d x} ( x ^{2} - 9 ) x}{( x ^{2} - 9 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} - 9) = 2 x

= 6 \cdot \frac{1 \cdot ( x ^{2} - 9 ) - 2 xx}{( x ^{2} - 9 ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot ( x ^{2} - 9 ) - 2 xx}{( x ^{2} - 9 ) ^{2}} : \frac{6 ( - x ^{2} - 9 )}{( x ^{2} - 9 ) ^{2}}

= \frac{6 ( - x ^{2} - 9 )}{( x ^{2} - 9 ) ^{2}}

y^{^{'}} = (3 x - 2) (30 x + 29)

im pl i c i t \frac{d y}{d x}, 9 x^{2} + y^{2} = 1

x \to - \infty lim (x^{2})

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 12 x^{2}

\int \frac{( 2 x + 11 )}{x ^{2} + x - 6} d x

What is the derivative of (6x/(x^2-9)) ?
The derivative of (6x/(x^2-9)) is (6(-x^2-9))/((x^2-9)^2)
What is the first derivative of (6x/(x^2-9)) ?
The first derivative of (6x/(x^2-9)) is (6(-x^2-9))/((x^2-9)^2)